Problem: Rewrite as a simplified fraction. ${0.\overline{40} = {?}}$
Answer: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}100x &= 40.404...\\ 1x &= 0.404...\end{align*}}$ Subtracting the two equations, we have: ${99x = 40}$ ${x = \dfrac{40}{99}} $